Long directed (s,t)-path: FPT algorithm

Given a digraph G, two vertices s,t∈V(G) and a non-negative integer k, the Long Directed(s,t)-Path problem asks whether G has a path of length at least k from s to t. We present a simple algorithm that solves Long Directed(s,t)-Path in time O⋆(4.884k). This results also in an improvement upon the previous fastest algorithm for Long Directed Cycle.